1. 2. 絵解き解説：フラウンホーファー回折 3. 5. 絵解き解説： …

1 1. 2. 3. 4. 5. 6. 7. diffraction 1. diffraction: the spreading of waves diffraction limit 2. 3. Rayleigh criterion Abbe diffraction limit for a microscope 1 2 903 Fresnel diffraction ()() ()

2 22211111122 12 1,,,allu x ydx dy u x y hxx yy = Fraunhoferdiffraction [ ][ ]21212112,1uhFuuFuh = == 12212121,ikzD ze iz ()21212 1 11,,1D zh xy ()()() ()()21 21122 2 212 2 21 1 1 1 1 12 1 1, ,,,ikxx yyzallu x yhx ydx dy u x y hx ye + = ()()()()21 2112222122211111,, ,ikxx yyzallu x yhx ydx dy u x y e += ( )()[]221222112122121 12*,ikxyzuu hh xy euh F uh +=== 3[]()() ()()()() () ()21 212112121 12212 2 21 1 1 1 1 12 1 1*122211011 12111211*,,,,, ,,ix yallalluu hh F uhhx ydx dy u x y hx yehdxdy u xy h xyh xy +== = = ()()()()[ ]21 2121 2122122211011120,,ix yix yallehdx dy u x y ehFu + + == ()()()() ()

3 221112*2111 0 110 1112 11, ,,,ikxyfzfu xy u xyeu xyh xy +== u1 u0 1 0 903-11 904 12zf=0u[ ]0Fu [ ][ ]*212012 20uhFuhuFu = =*12h 1u2u( )()2212212,ikxyzh xy e+= 4 903 D 12zf= ()()1110 1110,lim, ,u xyu xyz =+1zz=2zz=()222,u xy ()111,u xy ()0 11,u xy ()()0 110 1110,lim, ,u xyu xyz = ()

4 0 11,u xy 5 5 2121Dz 2121Dz 12z12z 90312zf= 2 2Da= ()

5 111,u xy2121Dz [ ]121hFu 12z()222,u xy 2Da=()2221111 12,102u x yfor xyaotherwiseDaSa =+ === 2Da= 6 903-14 ()()()()()()()()1221 21122221 212 212122221222111111221 1 1 1 112 2 2,, ,,,ikikzxx yyzallikikxx yyx yzzalleu x yhx ydx dy u x y eizdx dy u x y ehx ye + ++= = 212221,hIu= 7 1,21,2cos ,siniiiiiixy ==== 904-11 xy(),xy ( )( )1222122,JuSkaz == Bessel function 8 ( )( )221222122,Jukaz = ( )12J ( )

6 212J = 2121Dz 2121Dz Airy disk 2Da= 9 ( )( )( )2212221212, 20 JukazJ = == = ( )12J ( )212J = === = the first dark ring 10 2121Dz 2121Dz 12z12z 12zf= = === 2Da= 11 ( )

7 11112uforDa = =2121Dz 12z ( )( )221222122, = ( )222u ()11u 2Da= ()()()()21 212 11 212121221 12122112221 21 211212211 2cos21 111 1 100,2cos1212022cos cos sin sincosikikxx yyazzallzkkxxzkixzxx yydx dy u ed d ezzxdxd ekk + == = +=+= = ( )( )( )( )( )2221221221222cos1200222cos1200002212101 021221222akaixzkaixzkazzdx xd ekzJxdedxxJxkzddxJ xxJ xdxxJ xdxkdx = = = 12 Bessel function 13 ( )122121212122212121212022121212121222121 1222121221222222ikzkazikzikzikzzzkkexJ xaJakkzzizzzekk eaJaaJ kaizkkzzizeakaiz = == = ()

8 121221 2112222111212121222221221212121212211221 11212122221,,ikzikzikxx yyzallJ kaJ kaJ kazzzeaaaeizizkakakazzzJ kazdx dy u eSSazkaz + == == 14 12zf= ()()11111110,lim, ,u xyu xyz =+1zz=2zz=()222,u xy ()111,u xy ()0 11,u xy ()()0 110 1110,lim, ,u xyu xyz = ()0 11,u xy ()1122*uhu 9032Da= 15 2121Dz 2121Dz 12z12z 90312zf= 2 2Da= 2 212@zf = 16

9 904-7 ==== 212@zf = = = the first dark ring( )212J 17 2 2Da=f ( )( )2212222,Jukaf = =NA=sin ===== = numerical aperture 904-9 a 01zf=()() ()2 11*1111112,,,u xyu xyh xy =()322,u xy ()000,u xy ()111,u xy 12zf= ()()01 12000322,,?

10 Zz fu xyu xy= = ()()()11101011,*,u xyu h xy = ()()()32222122,*,u xyu h xy = ( )()0122012,ikxyzh xy e+=( )()1222122,ikxyzh xy e+= 18 904-18 01zf=()322,u xy ()000,u xy ()111,u xy 12zf=()()()11101011,*,u xyu h xy = ()()()3222211112,,,u xyh xyFu x y = 19 ()()0122012,ikxyzh xy e+=()()1222122,ikxyzh xy e+= () ()()() ()111011010 00 0 01 0 1 001, *,,,allu xyu h xydx dy u x y hxx yy == () ()()()()322222221212111, *,,,u xyu h xyh x y Fu x y = = ()()()221212233323122233,ikikxyxyzfzfh xy ee++== ()()()2201